The Alkali-Silica Reaction (ASR) in concrete is a chemical reaction, which produces an expansive product, generally called “ASR gel”, and causes cracking and damage in concrete over time. Affecting numerous infrastructures all around the world, ASR has been the topic of much research over the past decades. In spite of that, many aspects of this reaction are still unknown. In this numerical-investigation paper, a three-dimensional concrete meso-structure model is simulated using the finite-element method. Coarse aggregates, cement paste, and ASR gel are explicitly represented. A temperature dependent eigen-strain is applied on the simulated ASR gel pockets to capture their expansive behavior. This applies pressure on the surrounding aggregates and the cement paste, leading to cracks initiation and propagation. Free expansion of concrete specimens due to ASR is modeled and validated using experimental data. Influence of different key factors on damage generation in aggregates and paste and macroscopic expansion are discussed.